Determination of the Equilibrium Constant
Kyle Miller
December 11, 2006
1
Purpose
The purpose of this experiment is to determine the equilibrium constant for the reaction
Fe3+ + SCN− FeSCN2+ and to see if the constant is indeed the same under different
conditions.
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Procedure
First, reference solutions are made by mixing an excess of Fe3+ ions with known amounts
of SCN− ions. We then assume that the reactions are driven to completion due to Le
Chtelier’s Principle, so they contain a known concentration of FeSCN2+ ions. Second, test
solutions are made by mixing a constant amount of Fe3+ ions with varying amounts of
SCN− ions, which contain an unknown concentration of FeSCN2+ ions.
Then, the absorbance of the solutions are measured with a spectrophotometer. With the
reference solution’s absorbances, a calibration curve is made to then determine the concentrations of the test solutions. Then, with the calculated concentrations, the equilibrium
constant can be calculated.
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Data
The following data were collected:
1
3.1
Reference Solutions
Sample
Reference #1
Reference #2
Reference #3
Reference #4
Reference #5
3.2
Absorbance
0.233
0.299
0.409
0.524
0.600
Test Solutions
Sample
Test #6
Test #7
Test #8
Test #9
Test #10
4
[FeSCN2+ ]
4.0 × 10−5
6.0 × 10−5
8.0 × 10−5
1.0 × 10−4
1.2 × 10−4
[Fe3+ ]
1.0 × 10−3
1.0 × 10−3
1.0 × 10−3
1.0 × 10−3
1.0 × 10−3
[SCN− ]
2.0 × 10−4
4.0 × 10−4
6.0 × 10−4
8.0 × 10−4
1.0 × 10−3
Absorbance
0.233
0.412
0.568
0.792
0.985
Calculations
Using the method of least squares with the absorbance of the reference solutions, we can
find that
A = 5010 · [FeSCN2+ ] + 0.011
(1)
Where A is the absorbance for each [FeSCN2+ ]. This curve can also be written for the
concentration.
A − 0.011
[FeSCN2+ ] =
(2)
5010
Using this equation on each test solution absorbance, we can find the unknown [FeSCN2+ ]eq
concentrations. For example, with the absorbance of 0.233, the [FeSCN2+ ]eq = 0.233−0.011
=
5010
−5
4.4 × 10
Since each compound in the reaction is used or made in a 1:1 ratio, they will decrease or
increase (respectively) by the same amount. So, let [FeSCN2+ ] increase by x, then [Fe3+ ]
will decrease by x. Then, since [FeSCN2+ ] is starting at 0 for the experiment, the x is the
final concentration at equilibrium. For example, if [FeSCN2+ ] gets to be 4.4 × 10−5 , [Fe3+ ]
will be 1.0 × 10−3 − 4.4 × 10−5 = 9.6 × 10−4
With the same logic, we can find [SCN− ]eq which is the initial concentration of SCN− less
the change in [FeSCN2+ ]. This is, for example, 2.0 × 10−4 − 4.4 × 10−5 = 1.6 × 10−4
2
According to known rules, the equilibrium constant for this reaction is
Kp =
[FeSCN2+ ]
[Fe3+ ][SCN− ]
(3)
Then, using calculations from the results table, we can find the Keq values for each test
−5
solution. For example, for test solution #6, the Keq = (9.6×104.4×10
−4 )(1.6×10−4 ) = 290
The mean of the Keq values is
P
Keq
5
The average deviation of the Keq is
4.1
= 280
P
|Keq −280|
5
= 16
Results
Sample
Test #6
Test #7
Test #8
Test #9
Test #10
[FeSCN2+ ]eq
4.4 × 10−5
8.0 × 10−5
1.1 × 10−4
1.6 × 10−4
1.9 × 10−4
[Fe3+ ]eq
9.6 × 10−4
9.2 × 10−4
8.9 × 10−4
8.4 × 10−4
8.1 × 10−4
[SCN− ]eq
1.6 × 10−4
3.2 × 10−4
4.9 × 10−4
6.4 × 10−4
8.1 × 10−4
Keq
290
270
250
300
290
Mean: 280
Average Deviation: 16
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Discussion
1. The equilibrium constant is a quantity which characterizes an equilibrium in a reaction
and is based on the final concentrations of involved compounds. The value was constant for
all of the experiments (within a good margin of error). It should be consistent because this
constant is defined to be the relation between all concentrations of involved compounds at
chemical equilibrium.
2. The calculated value of the equilibrium constant indicates that there are mostly products
since it is 280 > 1. Also, since 280 is quite large (compared to the Haber process which
has a K of about 30), it should prefer the products.
3. A spectrophotometer is a device that measures the amount of light that can pass through
a given substance. In this experiment, we used it to determine the percent absorbance for
each solution. The reference solutions were obtained by mixing a known amount of SCN−
in an excess of Fe3+ so that we could assume that the reaction went to completion and
we would have a known amount of FeSCN2+ . We can then find the absorbances of the
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reference solutions to create a function that relates concentration to absorbance which can
then be applied to the unknown concentrations with the measured absorbances to calculate
the unknown concentration.
4. The spectrophotometer should not be set to the same color as that of the solution because
the visible color is that which is transmitted which mean none is absorbed. Another color’s
absorbance, such as the complement of the solution’s color, such as cyan (since the complex
ion is a red), or the components of cyan (green and blue), would probably change with
different concentrations because it is a color that must be absorbed to only allow red
through. In this experiment, 450nm light was used, which corresponds to blue. Since the
complex ion is red, this blue light will be absorbed and can then be measured.
5. The precision indicates that the equilibrium constant is indeed constant for the experi16
ment because it is such a small percentage of the mean Keq . It is only 280
= 5.7% of the
mean constant. This means that the calculated Keq for each solution is very close to each
other and that, for allowing for experimental error, they really are equal (noting that they
seem to be randomly larger or smaller than the mean without any correlation to any of
the concentrations that could otherwise explain this behavior).
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